In philosophy, specifically in the area of modal metaphysics, counterpart theory is an alternative to standard (Kripkean) possible-worlds semantics for interpreting quantified modal logic. Counterpart theory still presupposes possible worlds, but requires that individuals exist in only one world. The standard account of possible worlds assumes that a modal statement about an individual (It is possible that x is y) means that there is a possible world, W where the individual x has the property y; in this case there is only one individual, x, at issue. On the contrary, counterpart theory supposes that this statement is really saying that there is a possible world, W where -- not x itself, but rather a distinct individual x' different from x but nonetheless similar to x
So, when I state that I might have been a banker (rather than a philosopher) according to counterpart theory I am saying not that I exist in another possible world where I am a banker, but rather my counterpart does. Nevertheless, this statement about my counterpart is still held to ground the truth of the statement that I might have been a banker.
The form of the theory most commonly cited was developed by David Lewis, first in a paper and later in his book On The Plurality of Worlds. The requirement that any individual exist in only one world is to avoid what Lewis termed the "problem of accidental intrinsics" which (he held) would require a single individual to both have and simultaneously not have particular properties.
In addition, counterpart theoretic formalization of modal discourse eschews the formal use of modality operators (necessarily, possibly) in favor of quantifiers that range over worlds and 'counterparts' of individuals in those worlds.